Establishing and Understanding Adsorption−Energy ScalingRelations with Negative SlopesHai-Yan Su,†,# Keju Sun,‡,# Wei-Qi Wang,† Zhenhua Zeng,† Federico Calle-Vallejo,*,§

and Wei-Xue Li*,†,∥

†State Key Laboratory of Molecular Reaction Dynamics, State Key Laboratory of Catalysis, Dalian Institute of Chemical Physics,Chinese Academy of Science, Dalian 116023, China‡Key Laboratory of Applied Chemistry, College of Environmental and Chemical Engineering, Yanshan University, Qinhuangdao066004, China§Leiden Institute of Chemistry, Leiden University, Einsteinweg 55, 2333 CC Leiden, The Netherlands∥College of Chemistry and Material Sciences, Hefei National Laboratory for Physical Sciences at the Microscale, iChEM, CAS Centerfor Excellence in Nanoscience, University of Science and Technology of China, Hefei 230026, China

*S Supporting Information

ABSTRACT: Adsorption−energy scaling relations are widely used for the design of catalyticmaterials. To date, only linear scaling relations are known in which the slopes are positive.Considering the adsorption energies of F, O, N, C, and B on transition metals, we show herethat scaling relations with negative slopes also exist between certain adsorbates. The origin ofsuch unconventional scaling relations is analyzed in terms of common descriptors such as d-band center, work function, number of outer electrons, electronic charge on the adsorbates,integrated crystal orbital overlap populations, and crystal orbital Hamilton populations.Conventional scaling relations are formed between adsorbates such as F, O, N, and C, whichcreate ionic-like bonds with surfaces. Conversely, anomalous scaling relations are establishedbetween those and covalently bound adsorbates such as B. This widens the theory ofadsorption−energy scaling relations and opens new avenues in physical chemistry andcatalysis, for instance, in direct borohydride fuel cells.

I t is widely accepted that the adsorption properties oftransition-metal surfaces are determined by their geometric

and electronic structures.1 Such extended agreement came afternumerous works reporting correlations between structuralparameters, adsorption energies, and catalytic activities.2−9

Those “structure−energy” relations are complemented by avariety of “energy−energy” relations, such as Brønsted−Evans−Polanyi relations,10−12 bulk−surface relations,13 and adsorp-tion−energy scaling relations,4,14−18 which have enormouslyfacilitated the in silico design of new materials because of theirsimplicity.1,16 The adsorption energies of species 2 scale withthose of species 1 as follows

Δ = Δ +E m E b1 2 (1)

where b is a constant that depends on surface coordination.15

So far, m has always been found to be positive, as in someapproaches it is estimated as the ratio between the lack ofbonds of species 1 and 2 to reach the octet4,15 or as the ratio ofthe bond orders in other approaches.16,17,19

Analyzing the density functional theory (DFT) adsorptionenergies of F, O, N, C, and B on the close-packed surfaces of 4dand 5d transition metals, we will show here for the first timethat negative slopes are possible in scaling relations. Thisintriguing phenomenon is related to significant differences inthe metal−adsorbate bonds made by species 1 and 2 in eq 1.

For completeness, we will analyze conventional andunconventional scaling relations altogether. Figure 1 showsthe scaling relations between the most stable adsorptionenergies of N and the other adsorbates under study on theclosest-packed surfaces of 4d and 5d metals. While the scalingbetween F, O, C, and N is normal (m > 0), B and N exhibit anatypical negative slope (see Table S14 and Figure S9 in theSupporting Information (SI)). Hence Figure 1 raises animportant question: How can one rationalize negative slopesin adsorption−energy scaling relations?To address this question, we resort to a mathematical

formulation of scaling relations used before to understand thenature of their slope and offset,4,15 noting that other authorshave considered alternative bond-order formulations.16,17,19

Within this approach, ΔE1 and ΔE2 are a function of a set ofsurface or adsorbate electronic-structure parameters, denoted{ωi}

ω αΔ = +E F({ })i1 1 (2)

ω αΔ = +E G({ })i2 2 (3)

Received: October 19, 2016Accepted: December 5, 2016Published: December 5, 2016

Letter

pubs.acs.org/JPCL

© 2016 American Chemical Society 5302 DOI: 10.1021/acs.jpclett.6b02430J. Phys. Chem. Lett. 2016, 7, 5302−5306

where F and G are differentiable functions. Because α1 and α2depend on surface coordination,5,6,15 they are constant here, aswe only consider adsorption on closest-packed surfaces.Finding the parameters that belong in the set {ωi} is

important to determine whether scalability is possible betweentwo adsorbates.4,15 Thus, as part of {ωi} we consider here somewell-known descriptors: d-band center (εd), work function (Φ),excess Bader charge on the adsorbates,20 number of “outerelectrons” (NM, equivalent in metals to the number of valenceelectrons3), crystal orbital overlap population (coop), andcrystal orbital Hamilton population (cohp) integrated to theFermi level (Figures S5−S7).21,22 Figure 2 shows that those

descriptors are all linear functions of NM, that is, {ωi} = H(NM).Plausible arguments justify the relationships in this Figure, asdiscussed in detail in Section S5. Note in passing that thedescriptors in Figure 2 require self-consistent calculations to beestimated, but NM gives the highest predictive accuracy (TableS12).The adsorption energies (ΔEADS) of 2p atoms appear in

Figure 3 as a function of NM (see also Tables S5 and S13).

While F, O, N, and C bind more weakly as NM increases, in linewith previous observations,3−6 the opposite is true for B(Figure 3, inset). Therefore, the trends in ΔEADS depend notonly on the nature of the metals, as traditionally accepted, butalso on the adsorbates. This is important because mostdescriptors do not incorporate adsorbate features, asdescriptor-based analyses aim at predicting ΔEADS using theproperties of clean surfaces only.1

Because NM scales with εd, Φ, Bader excess charge, andintegrated coop/cohp, all descriptors capture the adsorption−energy trends similarly (Figures S1−S4, Tables S6−S11). Note,however, that B is always atypical, as the slopes of itscorrelations have opposite signs compared with the others. Insummary, Figures 1 and 2 show that numerous descriptors andadsorption energies depend linearly on NM (see also SectionS2), so eqs 2 and 3 are simplified as follows

λΔ = +E f N( )1 M 1 (4)

λΔ = +E g N( )2 M 2 (5)

Where f, g are differentiable functions and λ1, λ2 are constants.The scaling relation in eq 1 is fulfilled if f and g areproportional: f(NM) = m g(NM),

4,15 as exemplified in Figure 2.If both f ′ and g′ are definite positive or negative (where f ′ = ∂f/∂NM, g′ = ∂g/∂NM), then m > 0, which corresponds toconventional scaling relations (e.g., ΔEN vs ΔEC, ΔEO,ΔEF).

1−9,14−16,23−26 Conversely, if f ′ is definite positive andg′ is definite negative or vice versa, m < 0, as for ΔEB versusΔEN.

Figure 1. Normal scaling relations between the adsorption energies(ΔEADS) of N and 2p atoms. Inset: anomalous scaling relationshipbetween ΔEB and ΔEN (see also Figure S9). The equations of thelinear fits appear in Table S14.

Figure 2. Relationships between various descriptors and the metal’snumber of outer electrons (NM). (a) Surface d-band center (εd); (b)work function (Φ); (c) excess Bader charge on the adsorbates; and (d)integrated crystal orbital overlap population (coop) upon 2p atomadsorption.

Figure 3. Adsorption energies of 2p atoms as a function of the numberof outer electrons of transition metals. Inset: Data for B. ReportedΔEADS are those of the most stable adsorption sites; see Tables S5 andS13.

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After mathematically outlining the existence of scalingrelations with negative slopes, it is important to determinewhat distinguishes B chemically from the other adsorbates. Todo so, we first resort to the qualitative explanations ofmolecular-orbital theory.27 The interaction between adsorbateA and metal M can be classified in the four categories in Figure4a−d. If the orbital energy levels of A and M (for M, the energylevel represents relevant d and s states around the Fermi level)are largely different (Figure 4a), then the interaction is ionic. Asthe energy-level difference between A and M decreases (Figure4b), covalent interactions are strengthened. However, thebonding is still mainly ionic, corresponding to the interactionbetween transition metals and electronegative atoms (e.g., F,O). The differential charge density maps (Figure 4e) showconsiderable charge withdrawal from Zr or Rh by F and O,indicative of mostly ionic bonds. When the energy-leveldifference decreases (Figure 4c), the orbital mix is larger,leading to stronger covalent interactions. This is the case ofbonds between transition metals and less electronegative atoms(e.g., B). Figure 4e shows that considerable charge builds upbetween Zr or Rh and B, meaning that their bonds are largelycovalent. For N and C, both ionic and covalent bondingcontribute significantly. Finally, for A and M at the same energylevel, the orbital mixture is maximal and the bonding is purelycovalent (Figure 4d). The trends in Pauling’s ionicity28 for Zror Rh bonds with 2p atoms in Figure S8 agree with the analysisin Figure 4.

Furthermore, Figure 4 suggests that dissimilar orbitaloverlaps lead to ionic and covalent bonds that cause differentscaling relations (Figure 1). Thus orbital overlap is essential toquantitatively distinguish between B, C, N, O, and F bondswith surfaces. Figure 5 shows the integrated coop values versusthe adsorbates’ number of outer electrons (NA). A nearly linearcorrelation is observed between integrated coop and NA for F,O, N, and C. However, B deviates significantly, as shown byΔcoop. Interestingly, Δcoop is inversely proportional to NM sothat late transition metals set off less than the early ones (Figure5, inset), justifying the negative slope in Figure 1. An analogousexplanation is obtained from integrated cohp in Section S5.Hence simultaneously using adsorbate and metal descriptors(NA, NM), we conclude that B-metal bonds are qualitatively andquantitatively different from the other adsorbate−metal bondsstudied.In conclusion, classifying metal−adsorbate bonds into ionic

and covalent helps rationalize conventional and unconventionaladsorption-energy scaling relations. Conventional relations areobserved between highly electronegative adsorbates such as F,O, N, and C. The covalence of B-metal bonds introducesnegative slopes in its scaling relations with those adsorbates.These results and others7 widen the state of the art in scalingrelations and open new avenues, for instance, in the design ofbetter catalysts for direct borohydride fuel cells.29

Figure 4. Interactions between adsorbate A and metal M based on Hoffmann’s model.27 The energy-level difference between A and M decreasesprogressively from (a) to (d). F and O bonding correspond to (b), B bonding to (c), and N and C are in between. (e) Differential charge densitymap for adsorption of 2p atoms on Zr(0001) and Rh(111). Yellow, red, gray, brown, light-green, dark-green and maroon spheres represent F, O, N,C, B, Rh, and Zr, respectively. Blue and yellow-red isosurfaces indicate charge depletion and accumulation. The 2D profile is a cut along a Rh/Zr−adsorbate bond.

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■ METHODSAll adsorption energies (ΔEADS) were calculated using VASP30

with PBE.31 (2 × 2) 5-layer (111), (0001), and (110) slabs forfcc, hcp, and bcc transition metals were used, separated by 15 Åof vacuum. The two bottommost layers were fixed at the bulkdistances, and the three topmost layers and the adsorbates werefully relaxed. The Brillouin zones were sampled with 5 × 5 × 1Monkhorst−Pack grids.32 The plane-wave cutoff was 400 eV.ΔEADS was calculated using the most stable adsorptionconfigurations (Table S13) relative to the clean surfaces (E*)and the isolated atoms (EA)

Δ = − * −*E E E EA A A (6)

■ ASSOCIATED CONTENT*S Supporting InformationThe Supporting Information is available free of charge on theACS Publications website at DOI: 10.1021/acs.jpclett.6b02430.

(1) DFT/experimental Φ and lattice constants oftransition metals, experimental first ionization energiesfor metals and adsorbates. (2) ΔEADS versus variousdescriptors. (3) Data and correlations. (4) Adsorptionsites. (5) More about Figures 2 and 4, integrated cohp.(6) Additional scaling relations. (PDF)

■ AUTHOR INFORMATIONCorresponding Authors*F.C.-V.: E-mail: f.calle.vallejo@chem.leidenuniv.nl.*W.-X.L.: E-mail: wxli70@ustc.edu.cn.ORCIDFederico Calle-Vallejo: 0000-0001-5147-8635Wei-Xue Li: 0000-0002-5043-3088Author Contributions#H.-Y.S. and K.S. are equally contributing authors.NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSWe acknowledge funding from the Natural Science Foundationof China (21273224, 21321002, 21225315, 91421315), Na-tional Basic Research Program of China (2013CB834603),“Strategic Priority Research Program” of the Chinese Academyof Sciences (XDA09030101), The Netherlands Organizationfor Scientific Research (NWO) through Veni project722.014.009.

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Figure 5. Relationship between integrated coop and the adsorbate’snumber of outer electrons (NA). Inset: Δcoop (deviations in coop fromthe linear trends for B) as a function of the metals’ number of outerelectrons (NM).

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